Question

(-3,5-1 5/6):1 4/9-3 3/8*(-5 1/3)​

Answer 1

$( - 3.5 - 1 \frac{5}{6} ) + 1 \frac{4}{9} - 3 \frac{3}{8} \times ( - 5 \frac{1}{3} ) = ( - \frac{35}{10} - \frac{11}{6} )+ \frac{13}{9} - \frac{27}{8} \times ( - \frac{16}{3} ) = ( \frac{ - 105 - 55}{30} ) + \frac{13}{9} + \frac{27 \times 16}{8 \times 3} = - \frac{160}{30} + \frac{13}{9} + 18 = \frac{ - 480 + 130}{90} + 18 = - \frac{35}{9} + 18 = \frac{ - 35 + 162}{9} = 14 \frac{1}{9}$

Answer 2

To solve the expression (-3, 5-1 5/6):1 4/9 - 3 3/8 * (-5 1/3), we should follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders (i.e., powers and square roots, etc.), Multiplication and Division (left-to-right), and Addition and Subtraction (left-to-right). Let's break it down step by step:

1. Start with the parentheses: (-3, 5-1 5/6):1 4/9 - 3 3/8 * (-5 1/3)

2. Simplify the subtraction inside the parentheses: (-3, 3/6):1 4/9 - 3 3/8 * (-5 1/3)

3. Simplify the fraction inside the first set of parentheses: (-3, 1/2):1 4/9 - 3 3/8 * (-5 1/3)

4. Next, we need to evaluate the expression within the second set of parentheses (the mixed number): -5 1/3 can be written as -5 + 1/3. So, let's do that: (-3, 1/2):1 4/9 - 3 3/8 * (-5 + 1/3)

5. Now, calculate the multiplication on the right side of the expression: (-3, 1/2):1 4/9 - 3 * (-5 + 1/3) * 3/8

6. Continue simplifying within the parentheses: (-3, 1/2):1 4/9 - 3 * (-15/3 + 1/3) * 3/8

7. More simplification inside the parentheses: (-3, 1/2):1 4/9 - 3 * (-14/3) * 3/8

8. Now, calculate the multiplication within the parentheses: (-3, 1/2):1 4/9 - (-126/8)

9. Subtract the fraction on the right side from the fraction on the left side: (-3, 1/2) - (-126/8) = (-3, 1/2) + (126/8)

10. Add the fractions: (-3, 1/2) + (126/8)

Now, we need to convert the mixed number (-3, 1/2) into an improper fraction. To do this, we multiply the whole number (-3) by the denominator (2) and add the numerator (1):

= [(-3 * 2) + 1] / 2 = (-6 + 1) / 2 = -5/2

So, the expression becomes:

(-5/2) + (126/8)

Now, simplify further by finding a common denominator, which is 8:

(-5/2) + (126/8)

To have a common denominator, multiply the numerator and denominator of (-5/2) by 4:

= (-10/4) + (126/8)

Now, both fractions have a common denominator of 8:

= (-10/8) + (126/8)

Now, you can add the fractions:

= (-10 + 126)/8

= 116/8

Finally, simplify the fraction:

= 29/2

So, the value of the expression is 29/2.